Particle-surface interactions in a uniform electric field

TL;DR

This paper calculates electrostatic forces on a spherical particle near a surface under uniform electric fields, revealing how conductivity ratios and field directions influence attraction or repulsion.

Contribution

It provides an analytical solution for particle-surface electrostatic interactions in a leaky dielectric model using bipolar coordinates and Legendre polynomial series.

Findings

Normal electric field causes always attractive forces.

Force magnitude depends on conductivity ratio.

Tangential electric field results in repulsive forces.

Abstract

The electrostatic force on a spherical particle near a planar surface is calculated for the cases of a uniform electric field applied in either normal or tangential direction to the surface. The particle and suspending media are assumed to be weakly conducting, so that that the leaky dielectric model applies. The Laplace equation for the electric potential is solved in bipolar coordinate system and the potential is obtained in terms of a series expansion of Legendre polynomials. The force on the particle is calculated using the Maxwell tensor. We find that in the case of normal electric field, which corresponds to a particle near an electrode, the force is always attractive but at a given separation it varies nontrivially with particle-suspending medium conductivity ratio; the force on a particle that is more conducting than the suspending medium is much larger compared to the force on a particle less conducing than the suspending medium. In the case of tangential electric field, which corresponds to a particle near an insulating boundary, the force is always repulsive.